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Research Article | Open Access

Zero-stability of waveform relaxation methods for ordinary differential equations

College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China

Academic Editor:Jingzhi Li

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Abstract

Zero-stability is the basic property of numerical methods of ordinary differential equations (ODEs). Little work on zero-stability is obtained for the waveform relaxation (WR) methods, although it is an important numerical method of ODEs. In this paper we present a definition of zero-stability of WR methods and prove that several classes of WR methods are zero-stable under the Lipschitz conditions. Also, some numerical examples are given to outline the effectiveness of the developed results.

Keywords

waveform relaxation methodszero stabilityordinary differential equationslinear multi-step methodsLipschitz conditions

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Electronic Research Archive
Volume 30 Issue 3,
March 2022
Pages 1126-1141
DOI: 10.3934/era.2022060

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Cite this article:
Fan Z. Zero-stability of waveform relaxation methods for ordinary differential equations. Electronic Research Archive, 2022, 30(3): 1126-1141. https://doi.org/10.3934/era.2022060

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Received: 09 October 2021
Revised: 18 January 2022
Accepted: 27 February 2022
Published: 15 March 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)